tangent circles

Question

line segements PA and Pb are tangeng segments from point P

1.)if OA=6cm and PA=8cm find OP.

2.)If OP=13cm and PA=12cm find OA.

Answer 1

Tangent line

A line which touches a circle at just one point.the radius to the point of tangency is always perpendicular to the tangent line.

Here the line segments are PA, PB are tangent segments from point P

Then there form PAO, PBO are right angle triangles.

1) From Pythogerous therom (hypotenuse)^2 = (adjacent side)^2+(opposite side)^2

OP^2 = Ap^2+OA^2

OP^2 = 64+36

100 = OP^2

OP = 10

2) 169 = 144+OA^2

169-144 = OA^2

25 = OA^2

OA = 5